Light emitting diodes are to be driven at a constant current. Linear current sources are broadly used for this purpose, as they are cheap and highly accurate. Further, the linear current sources can be switched on and off quickly, a characteristic being advantageous for implementing pulse width modulation (PWM) dimming. Amplitude modulation (AM) dimming is also easy to implement by linear current sources, wherein different current levels or current digital-to-analog converters are used. Typically, linear current sources are used in one dimensional (1D) and two dimensional (2D) dimmable backlight systems, since many independent current sources are required in those applications. Another approach consists in switch-mode solutions, which is, however, more expensive, but less power consuming. Linear current sources used for driving LED strings have only limited power efficiency, which is mainly due to voltage variations of the LEDs. These voltage variations find their origin in temperature dependence, spread, and aging. If a fixed voltage supply is used for driving the light emitting diodes of a string, the current sources being coupled in series to the LED strings may experience a large voltage. The large voltage entails a large power dissipation, which in turn requires the current sources to be suitable to withstand high temperatures. Accordingly, design considerations are to be made, which result in more devices and packages in parallel, additional heat sinking mechanisms, and generally, in a substantial increase in costs.